A293897 Sum of proper divisors of n of the form 3k+1.

0, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 5, 1, 8, 1, 5, 1, 1, 1, 15, 8, 1, 1, 5, 1, 14, 1, 12, 1, 11, 1, 21, 1, 1, 8, 5, 1, 20, 14, 15, 1, 8, 1, 27, 1, 1, 1, 21, 8, 36, 1, 18, 1, 1, 1, 40, 20, 1, 1, 15, 1, 32, 8, 21, 14, 23, 1, 39, 1, 18, 1, 5, 1, 38, 26, 24, 8, 14, 1, 71, 1, 1, 1, 40, 1, 44, 1, 27, 1, 11, 21, 51, 32, 1, 20, 21, 1, 57, 1, 40, 1, 35, 1, 70, 8

Offset: 1

Author

Antti Karttunen, Nov 06 2017

Keywords

• nonn
• easy

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000
• Index entries for sequences related to sums of divisors.

Crossrefs

Cf. A078181, A293901, A293895, A293898.

Programs

Mathematica

Table[DivisorSum[n, # &, And[Mod[#, 3] == 1, # != n] &], {n, 105}] (* Michael De Vlieger, Nov 08 2017 *)

PARI

A293897(n) = sumdiv(n,d,(d
				

Formula

a(n) = A078181(n) - ([n == 1 (mod 3)]*n).

G.f.: Sum_{k>=1} (3*k-2) * x^(6*k-4) / (1 - x^(3*k-2)). - Ilya Gutkovskiy, Apr 14 2021

Sum_{k=1..n} a(k) = c * n^2 + O(n*log(n)), where c = Pi^2/36 - 1/6 = 0.107489... . - Amiram Eldar, Nov 27 2023